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A Kingly Tour


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7 replies to this topic

#1 bonanova

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Posted 29 January 2013 - 07:42 AM

A king tours an nxn chessboard without visiting a square twice. Your opponent begins by placing the king in any corner. Thereafter, you and she alternate making legal moves of the king. A player loses when there is no previously unoccupied square available for a move.

For what n do you have a winning strategy?

Is there an n for which you have a winning strategy in the modified case where your opponent can make any move on her turn, while you are constrained to make legal king moves only?
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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#2 Prime

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Posted 29 January 2013 - 10:13 AM

Spoiler for For starters


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Past prime, actually.


#3 bonanova

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Posted 31 January 2013 - 11:42 AM

Spoiler for For starters

OK so far. How about n=8?


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#4 TimeSpaceLightForce

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Posted 31 January 2013 - 04:34 PM

This is like a Tron game with diagonals. Nice to play. The strategy is get in the middle first.


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#5 Prime

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Posted 01 February 2013 - 03:17 AM

I can’t find any simple formal description for the strategy. It appears, for an even “n” - you win; for an odd - she does.

Spoiler for Diagram

Interesting question is: with an even n, can she have a winning strategy in the modified version, where she can jump the King to any available square?


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Past prime, actually.


#6 Prime

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Posted 01 February 2013 - 05:32 AM

And then you must watch out for traps

Spoiler for a trap

 


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Past prime, actually.


#7 k-man

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Posted 01 February 2013 - 03:27 PM

And then you must watch out for traps

Spoiler for a trap

Not really. Your next move is A6 and she loses.


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#8 Prime

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Posted 01 February 2013 - 07:22 PM

 


 

And then you must watch out for traps

Spoiler for a trap

Not really. Your next move is A6 and she loses.

True. My mistake.

Perhaps, the following could be thought of as a trap, though it's a stretch

Spoiler for a trap?

For any even n, you must win.


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Past prime, actually.





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